Use an Inverse Matrix to Find the Solution to the System

question 13

Multiple Choice

Use an inverse matrix to find the solution to the system.
-Two phone companies compete for customers in a city. Company 1 retains $3 / 4$ of its customers and loses $1 / 4$ of its customers to Company 2 . Company 2 retains $5 / 6$ of its customers and loses $1 / 6$ to Company 1 . If we represent the fraction of the market held last year by $\left[ \begin{array} { l } a \\ b \end{array} \right]$ , where $a$ is the number the that Company 1 had last year and $b$ is number that Company 2 had last year, then the number that each company will have this year can be found by t] following matrix equation.
$$\left[ \begin{array} { l } \mathrm { A } \\\mathrm { B }\end{array} \right] = \left[ \begin{array} { l l } 3 / 4 & 1 / 6 \\1 / 4 & 5 / 6\end{array} \right] \left[ \begin{array} { l } \mathrm { a } \\\mathrm { b }\end{array} \right]$$
If Company 1 has $\mathrm { A } = 90,000$ customers and Company 2 has $\mathrm { B } = 198,000$ customers this year, how many customers did Company 1 have last year?

• A) 76,000 customers
• B) 222,000 customers
• C) 72,000 customers
• D) 216,000 customers

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Definitions:

Product Features

are the distinct attributes or aspects of a product that provide value, meet customer needs, or differentiate it from competitors.

Operating Software

Programs or systems that manage the hardware of a computer and provide a platform for running application software.

Cell Phones

Portable electronic devices used for mobile communication, including voice calls, text messaging, and internet access.

Scenario Painting

The process of creating detailed and vivid descriptions of hypothetical situations to explore potential outcomes or decisions.